Penjelasan dengan langkah-langkah:

Penjelasan dengan langkah-langkah:

A.

\begin{gathered}\lim_{x\to0}\frac{2\tan(5x)}{7\tan(4x)}\\=\lim_{x\to0}\frac{2\sin(5x)}{\cos(5x)}.\frac{\cos(4x)}{7\sin(4x)}\\=\frac{2}{7}\lim_{x\to0}\frac{\sin(5x)}{\sin(4x)}.\frac{\cos(4x)}{\cos(5x)}\end{gathered}

x→0

lim

7tan(4x)

2tan(5x)

=

x→0

lim

cos(5x)

2sin(5x)

.

7sin(4x)

cos(4x)

=

7

2

x→0

lim

sin(4x)

sin(5x)

.

cos(5x)

cos(4x)

\begin{gathered}=\frac{2}{7}\lim_{x\to0}\frac{\sin(5x)}{\sin(4x)}.\lim_{x\to0}\frac{\cos(5x)}{\cos(4x)}\\=\frac{2}{7}.\frac{5}{4}.\frac{\cos(5.0)}{\cos(4.0)}\\=\frac{10}{28}.\frac{\cos(0)}{\cos(0)}\\=\frac{10}{28}\\=\frac{5}{14}\end{gathered}

=

7

2

x→0

lim

sin(4x)

sin(5x)

.

x→0

lim

cos(4x)

cos(5x)

=

7

2

.

4

5

.

cos(4.0)

cos(5.0)

=

28

10

.

cos(0)

cos(0)

=

28

10

=

14

5

B.

\lim_{x\to0}\frac{\sin(5x)-\sin(3x)}{2x}=\lim_{x\to0}\frac{\sin(5x)}{2x}-\lim_{x\to0}\frac{\sin(3x)}{2x}=\frac{5}{2}-\frac{3}{2}=\frac{2}{2}=1lim

x→0

2x

sin(5x)−sin(3x)

=lim

x→0

2x

sin(5x)

−lim

x→0

2x

sin(3x)

=

2

5

−

2

3

=

2

2

=1